Broadside Array Calculator

Broadside Array Calculator: Calculate Antenna Array Gain and HPBW

A Broadside Array Calculator helps estimate important characteristics of a uniform broadside antenna array from three basic inputs: the number of elements, element spacing relative to wavelength, and individual element gain. It calculates the main beam direction, progressive phase, idealized array-factor gain, estimated total gain, and approximate half-power beamwidth (HPBW).

A broadside array is designed so that its primary radiation beam points perpendicular to the axis along which the antenna elements are arranged. In the simplified model used by this calculator, the progressive phase is 0°, and the main beam direction is 90°.

The calculator is useful for preliminary antenna design, RF education, amateur-radio projects, and comparing different array configurations. It should be treated as an analytical estimation tool rather than a replacement for electromagnetic simulation or measurements.

What Is a Broadside Antenna Array?

A broadside antenna array is an antenna system consisting of multiple radiating elements arranged along an axis, with the strongest radiation directed approximately perpendicular to that axis.

The word broadside describes the direction of maximum radiation. Imagine several antenna elements arranged in a straight line. Instead of pointing the strongest beam along that line, a broadside configuration produces its principal beam outward from the side of the array.

The behavior of an antenna array depends on several factors, including:

• Number of antenna elements
• Distance between adjacent elements
• Operating wavelength
• Relative phase between elements
• Individual element radiation characteristics
• Amplitude distribution
• Feed network
• Mutual coupling

For the Broadside Array Calculator, the progressive phase is fixed at:

β = 0°

This means the elements are modeled with zero progressive phase difference. Under this simplified broadside assumption, the calculator reports the main beam direction as:

90°

The calculator also estimates array-factor gain using the number of elements and combines that value with the specified individual element gain.

Broadside Array vs. End-Fire Array

Broadside and end-fire arrays are two fundamental antenna-array configurations.

A broadside configuration is particularly useful when the desired coverage or communication direction is perpendicular to the physical line of antenna elements.

How the Broadside Array Calculator Works

The calculator uses three primary inputs:

1. Elements (N)
2. Element Spacing (d/λ)
3. Element Gain (dBi)

These values are used to estimate the array's idealized gain and beamwidth.

1. Number of Elements (N)

The number of elements represents how many antenna elements are included in the array.

The calculator requires an integer between 2 and 1024.

For example:

• 2 elements
• 4 elements
• 8 elements
• 16 elements
• 32 elements

Increasing the number of elements increases the idealized array-factor gain according to:

Array Factor Gain = 10 log₁₀(N)

For an 8-element array:

10 log₁₀(8) ≈ 9.03 dB

For a 16-element array:

10 log₁₀(16) ≈ 12.04 dB

This illustrates an important antenna-array principle: array-factor gain increases logarithmically with the number of elements rather than linearly in dB.

2. Element Spacing (d/λ)

Element spacing describes the distance between adjacent antenna elements relative to the operating wavelength.

Instead of entering spacing directly in meters or feet, this calculator uses a normalized value:

d/λ

where:

• d = physical spacing between adjacent elements
• λ = operating wavelength

For example:

• 0.25 means 0.25λ
• 0.5 means 0.5λ
• 0.75 means 0.75λ

If the spacing is entered as 0.5, the calculator interprets it as:

d = 0.5λ

Normalized spacing is useful because antenna-array behavior is strongly related to electrical size rather than physical dimensions alone.

The calculator limits the input to values between 0.01λ and 0.99λ.

3. Element Gain

The third input is the gain of an individual antenna element, expressed in dBi.

For example, you might enter:

2.15 dBi

The calculator then adds the idealized array-factor gain to this individual element gain.

The resulting estimate is:

Estimated Total Gain = Element Gain + 10 log₁₀(N)

This is a simplified calculation. Actual realized gain can differ because practical antenna arrays experience losses and electromagnetic interactions that are not included in this model.

Broadside Array Formulas Explained

Understanding the formulas behind the calculator makes it easier to interpret the results.

Broadside Progressive Phase

The calculator assumes:

β = 0°

Progressive phase describes the phase difference between successive antenna elements.

For the broadside configuration represented by this calculator, no progressive phase shift is applied from one element to the next.

The calculator therefore reports:

Progressive Phase = 0.00°

and:

Main Beam Direction = 90.00°

The 90° value represents the broadside direction using the calculator's angular convention.

Array Aperture in Wavelengths

The calculator determines an aperture measure using:

L/λ = N × (d/λ)

where:

• L/λ = calculated array-length measure in wavelengths
• N = number of elements
• d/λ = normalized element spacing

For example, if an array contains 8 elements with 0.5λ spacing:

L/λ = 8 × 0.5 = 4λ

The resulting electrical aperture is then used in the HPBW approximation.

One important point is that this calculator's aperture expression follows its implementation directly. In detailed antenna engineering, physical array length and element-to-element spacing are often defined using the number of intervals between elements, so users should not automatically interpret this value as the exact physical end-to-end dimension of a constructed array.

Broadside Array Gain Formula

The calculator estimates array-factor gain using:

G_array ≈ 10 log₁₀(N) dB

For example:

4 elements

10 log₁₀(4) ≈ 6.02 dB

8 elements

10 log₁₀(8) ≈ 9.03 dB

16 elements

10 log₁₀(16) ≈ 12.04 dB

32 elements

10 log₁₀(32) ≈ 15.05 dB

This is an idealized array-factor contribution used by the calculator. It should not be interpreted as the guaranteed measured gain of a physical antenna array.

Estimated Total Gain

The calculator combines the element gain with the estimated array-factor gain:

G_total ≈ G_element + 10 log₁₀(N)

Suppose an array has:

• 8 elements
• Element gain = 2.15 dBi

The array-factor gain is approximately:

10 log₁₀(8) = 9.03 dB

Therefore:

Estimated Total Gain = 2.15 + 9.03

Estimated Total Gain ≈ 11.18 dBi

This value represents the calculator's simplified estimate.

A real antenna could have lower realized gain because of feed-system losses, conductor losses, impedance mismatch, mutual coupling, phase errors, manufacturing tolerances, and other practical effects.

Broadside Array HPBW Formula

The calculator estimates half-power beamwidth using:

HPBW ≈ 50.76° / [N × (d/λ)]

HPBW stands for Half-Power Beamwidth.

It represents the approximate angular width of the antenna's main beam between the points where the radiation power has fallen by 3 dB from its peak.

The calculator also relates this to the aperture approximation:

HPBW ≈ 0.886 × (λ/L)

when expressed in radians.

The important relationship is:

HPBW ∝ 1 / [N × (d/λ)]

Therefore, increasing the calculated electrical aperture generally produces a narrower estimated main beam.

Understanding HPBW in a Broadside Array

HPBW is one of the most useful measurements for understanding antenna directivity.

A smaller HPBW means the main beam is narrower. A larger HPBW means the main beam is wider.

For example, an array with an estimated HPBW of approximately 12° has a much narrower main beam than one with an estimated HPBW of 40°.

The calculator uses:

HPBW ≈ 50.76° / [N × (d/λ)]

This means both the number of elements and normalized spacing affect the estimated beamwidth.

Increasing the number of elements

Increasing N increases the calculated aperture and therefore reduces the estimated HPBW.

Increasing spacing

Increasing d/λ also increases the calculated aperture and therefore reduces the estimated HPBW.

However, spacing cannot be considered independently from array-pattern behavior. Larger spacing can introduce unwanted pattern effects, including grating lobes under conditions not captured by this simplified calculator.

Consequently, a narrower calculated HPBW is not automatically evidence that a particular spacing is optimal.

Real-Life Example: Designing an 8-Element Broadside Array

Consider an RF engineer or amateur-radio operator evaluating an 8-element broadside array.

The design uses:

• Number of elements: 8
• Element spacing: 0.5λ
• Element gain: 2.15 dBi

Let's calculate the expected values.

Step 1: Calculate the Array Aperture Measure

The calculator uses:

L/λ = N × (d/λ)

Therefore:

L/λ = 8 × 0.5

L/λ = 4

So the calculator uses an electrical aperture measure of 4λ.

Step 2: Calculate Array-Factor Gain

The array-factor gain is:

10 log₁₀(8)

which is approximately:

9.03 dB

Step 3: Calculate Estimated Total Gain

The individual element gain is 2.15 dBi.

Therefore:

G_total = 2.15 + 9.03

G_total ≈ 11.18 dBi

Step 4: Calculate Estimated HPBW

Using:

HPBW = 50.76 / 4

we get:

HPBW ≈ 12.69°

Calculator Results

What does this mean?

The simplified model predicts that the array's main beam points in the broadside direction at 90°, with an estimated total gain of approximately 11.18 dBi and an HPBW of approximately 12.69°.

A designer could use these numbers as an initial reference when comparing array configurations.

However, a physical 8-element antenna would not necessarily produce exactly these results. Detailed simulation and measurement would be required to determine actual radiation characteristics.

Broadside Array Calculator Use Cases

The calculator can be useful across several antenna-design and learning scenarios.

Amateur Radio

Radio amateurs can use the calculator to explore how changing the number of elements and spacing affects an idealized array configuration.

For example, an operator can compare:

• 4-element array
• 8-element array
• 16-element array

and observe how the estimated array-factor gain changes.

The tool can also help illustrate why a larger electrical aperture tends to produce a narrower main beam.

RF and Microwave Engineering

For RF engineers, the calculator can serve as a preliminary estimation tool during antenna concept development.

It can help with early-stage questions such as:

• How many elements might be needed?
• How does changing spacing affect estimated HPBW?
• What happens to idealized array-factor gain when N increases?
• How does element gain contribute to the estimated total gain?

It is particularly useful before moving to more sophisticated electromagnetic simulation.

Electronics and Engineering Education

Broadside arrays are an effective way to learn fundamental antenna-array concepts.

Students can experiment with:

• Element count
• Electrical spacing
• Array gain
• Beamwidth
• Progressive phase
• Main-beam direction

Changing one variable at a time makes the relationship between array geometry and antenna performance easier to understand.

Antenna Prototyping

A designer developing an antenna prototype can use the calculator for a first-pass estimate before constructing the physical array.

The workflow might look like:

Concept → Calculator → EM Simulation → Prototype → Measurement → Optimization

This calculator fits primarily into the early concept and preliminary-design stage.

Comparing Array Configurations

Another useful application is configuration comparison.

For example, a designer can compare:

• 8 elements at 0.25λ
• 8 elements at 0.5λ
• 8 elements at 0.75λ

or compare:

• 4 elements
• 8 elements
• 16 elements

while keeping other inputs constant.

This provides a quick way to understand design trade-offs before committing to a particular physical configuration.

Why Element Spacing Matters

Element spacing is a critical parameter in antenna arrays.

If elements are placed closer together, the calculated electrical aperture becomes smaller for a fixed number of elements.

If the elements are spaced farther apart, the calculated aperture becomes larger.

Because the calculator uses:

HPBW ≈ 50.76° / [N × (d/λ)]

increasing spacing produces a smaller calculated HPBW.

However, antenna design is not simply a case of maximizing spacing.

Spacing influences the radiation pattern, sidelobes, and potential grating-lobe behavior. The acceptable spacing depends on factors such as array geometry, scan angle, frequency, and element radiation characteristics.

A spacing around 0.5λ is commonly used as a useful starting point in many array-design contexts, but it should not be treated as a universal optimum for every broadside array.

The calculator's input validation restricts spacing to less than 1λ as a simplified design guardrail. This should not be interpreted as a complete grating-lobe analysis.

Array Gain vs. Element Gain

One of the most important concepts to understand is the difference between element gain and array-factor gain.

Element Gain

Element gain describes the gain associated with one antenna element.

For example:

2.15 dBi

could be entered as the element gain.

Array-Factor Gain

The calculator estimates the array contribution using:

10 log₁₀(N)

For 8 elements:

9.03 dB

Estimated Total Gain

The calculator adds the two:

2.15 dBi + 9.03 dB = 11.18 dBi

This is a simplified estimate.

In a real array, the total realized gain can be affected by:

• Feed-line losses
• Connector losses
• Impedance mismatch
• Mutual coupling
• Phase errors
• Amplitude errors
• Conductor losses
• Dielectric losses
• Element-pattern interactions
• Mechanical tolerances

Therefore, calculator output should be viewed as a preliminary design estimate rather than a guaranteed measurement.

Small-Aperture Warning in the Calculator

The calculator includes an important safeguard for very small calculated apertures.

It computes:

N × (d/λ)

If this value is below 0.5, the calculator does not provide an HPBW value.

Instead, it displays a warning explaining that the array aperture is too small for the implemented HPBW approximation.

The reason is mathematical: applying the approximation to a very small aperture can produce an HPBW greater than 180°, which is not a meaningful result for this application.

The calculator therefore continues to provide:

• Main beam direction
• Progressive phase
• Array-factor gain
• Estimated total gain

but does not return an HPBW estimate.

How to address the warning

You can generally increase the calculated aperture by:

• Increasing the number of elements, or
• Increasing element spacing within the permitted range.

For example, if a configuration has a very small value of N × d/λ, adding more elements can increase the electrical aperture.

This warning is specifically a validity guard for the calculator's HPBW approximation. It should not be interpreted as a universal electromagnetic threshold for all antenna-array designs.

How to Use the Broadside Array Calculator

Using the calculator is straightforward.

Step 1: Enter the Number of Elements

Enter the number of antenna elements.

For example:

8

The value must be an integer of at least 2.

Step 2: Enter Element Spacing

Enter the spacing as a fraction of wavelength.

For example:

0.5

This represents:

0.5λ

Step 3: Enter Element Gain

Enter the gain of an individual element in dBi.

For example:

2.15 dBi

Step 4: Review the Results

The calculator provides:

Main Beam Direction

For this broadside model:

90.00°

Progressive Phase

0.00°

Array Factor Gain

Calculated using:

10 log₁₀(N)

Estimated Total Gain

Calculated using:

Element Gain + Array Factor Gain

Estimated HPBW

Calculated using:

50.76° / [N × (d/λ)]

provided that the calculated aperture meets the calculator's minimum condition.

Broadside Array vs. Other Antenna Array Types

Different antenna arrays use different geometries and phase relationships.

The Broadside Array Calculator is specifically designed for the simplified broadside case.

It does not calculate arbitrary beam steering or progressive phase values for a phased array.

If your objective is to steer a beam away from broadside, you need a model that includes the required phase progression and steering angle.

Limitations of the Broadside Array Calculator

The calculator is intentionally simple and fast. It is designed for preliminary calculations rather than full electromagnetic analysis.

It does not model:

• Mutual coupling between elements
• Detailed individual element radiation patterns
• Feed-network losses
• Phase imbalance
• Amplitude imbalance
• Ground-plane effects
• Nearby structures
• Reflections
• Polarization mismatch
• Manufacturing tolerances
• Frequency-dependent component behavior
• Complete sidelobe structure
• Full electromagnetic interactions
• Measured radiation patterns

This distinction is important.

Calculator estimate ≠ measured antenna performance.

A physical antenna array can behave differently from the idealized mathematical model.

For serious RF or microwave antenna development, the normal engineering workflow should include electromagnetic simulation and, where practical, physical measurement.

The calculator is best suited to:

• Initial design
• Educational analysis
• Configuration comparisons
• Quick gain estimates
• Preliminary beamwidth estimation

Frequently Asked Questions

What is a broadside array?

A broadside array is an antenna array arranged so that its principal radiation beam points approximately perpendicular to the axis along which the elements are arranged. In this calculator, the broadside beam direction is represented as 90°.

What does a Broadside Array Calculator calculate?

This calculator estimates the main beam direction, progressive phase, array-factor gain, estimated total gain, and half-power beamwidth based on the number of elements, normalized spacing, and individual element gain.

What is the broadside array gain formula?

The calculator uses:

Array Factor Gain ≈ 10 log₁₀(N) dB

where N is the number of elements.

The estimated total gain is:

Element Gain + 10 log₁₀(N)

What is the HPBW formula for a broadside array?

The calculator uses:

HPBW ≈ 50.76° / [N × (d/λ)]

This is an approximation based on the calculated electrical aperture.

What does β = 0° mean?

β represents progressive phase. A value of 0° means that the calculator assumes zero progressive phase between successive elements.

Why is the main beam direction 90°?

The calculator uses 90° as the broadside direction. With zero progressive phase, the simplified model places the principal beam perpendicular to the array axis.

How does increasing the number of elements affect gain?

According to the calculator's model, array-factor gain increases according to 10 log₁₀(N). Therefore, increasing the number of elements increases the idealized array-factor contribution logarithmically.

How does element spacing affect HPBW?

The calculator's HPBW formula is inversely proportional to N × (d/λ). Therefore, increasing spacing produces a narrower estimated HPBW when the number of elements remains constant.

Is 0.5λ spacing always the best choice?

No. Although 0.5λ can be a useful starting point for many array designs, there is no universal spacing that is optimal for every antenna. Array geometry, scan angle, element pattern, sidelobes, coupling, and other design requirements must be considered.

Can this calculator predict actual antenna gain?

No. It provides a simplified estimate based on element gain and the idealized array-factor relationship. Actual realized gain can be affected by losses, coupling, phase errors, feed networks, and other physical factors.

What happens if N × d/λ is below 0.5?

The calculator does not return an HPBW estimate because the implemented approximation is considered unsuitable for such a small calculated aperture. It instead displays a warning.

Can this calculator design a phased-array beam?

No. This calculator specifically assumes a broadside configuration with β = 0°. It does not calculate arbitrary beam-steering angles or progressive phase values.

Can I calculate an 8-element broadside array?

Yes. For example, entering 8 elements, 0.5λ spacing, and 2.15 dBi element gain produces an estimated array-factor gain of approximately 9.03 dB, estimated total gain of approximately 11.18 dBi, and estimated HPBW of approximately 12.69°.

Practical Broadside Array Design Tips

When using the calculator for preliminary antenna design, keep these points in mind:

• Start with a realistic number of elements.
• Compare multiple element counts before selecting a final configuration.
• Evaluate spacing in terms of wavelength.
• Use HPBW to understand the approximate main-beam width.
• Treat calculated gain as an idealized estimate.
• Don't assume that increasing spacing is always beneficial.
• Consider the effect of feed-system losses.
• Account for mutual coupling in detailed designs.
• Consider the actual radiation pattern of each element.
• Use electromagnetic simulation before manufacturing a complex array.
• Measure the finished antenna whenever accurate performance matters.

Pro Tip

Adding more elements can increase the idealized array-factor gain and narrow the calculated beam, but it can also increase mechanical complexity, feed-network requirements, cost, and sensitivity to implementation errors.

The best antenna design is therefore not necessarily the one with the maximum number of elements. It is the one that meets the required gain, beamwidth, physical-size, efficiency, and implementation constraints.

Conclusion

The Broadside Array Calculator provides a fast way to estimate fundamental characteristics of a simplified broadside antenna array. By entering the number of elements, element spacing in wavelengths, and individual element gain, you can calculate the broadside beam direction, zero progressive phase, array-factor gain, estimated total gain, and approximate HPBW.

The calculator uses β = 0° for the broadside configuration and estimates array-factor gain with 10 log₁₀(N). Its HPBW calculation is based on the electrical aperture represented by N × (d/λ).

For preliminary antenna design, these calculations can help you compare different array configurations and understand the relationship between element count, spacing, gain, and beamwidth.

However, the results are simplified estimates. Real antenna arrays are influenced by mutual coupling, feed losses, element patterns, phase and amplitude errors, ground effects, and construction details. For a production or high-performance antenna, the calculator should be followed by electromagnetic simulation and, where possible, physical testing.

Use the Broadside Array Calculator to quickly evaluate your antenna-array concept before moving to detailed simulation, prototyping, and measurement.